## Abstract

A new, to our knowledge, method for evaluating three-dimensional
flux distributions for general filament light sources is
presented. The main advantages of the developed model are its
generality and its simplicity. From plots of the emitted luminous
intensity, usually provided by the lamp’s manufacturer, in three
orthogonal planes a detailed account is given of how to establish flux
emission from the light source in any direction. The method
involves a selective smoothing procedure, a curve-fitting step, and a
final interpolation. A full model is developed for a typical
commercial filament bulb (Philips, Model P21W Inco K) that is quite
common in many industrial applications. A fourth intensity plot,
usually provided by the lamp’s manufacturer, is used to validate the
model. To confirm the validity of the model further, we present an
industrial application (the photometric simulation of a car
taillight) that uses the modeled Philips Model P21W source. A
comparison between simulated data obtained by use of the developed P21W
model and measured results at our industrial partner’s laboratories
reinforces the proposed source model.

© 1999 Optical Society of America

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### Equations (5)

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(1)
$$\mathrm{\xi}=\frac{{f}_{\mathit{YZ}}\left(\mathrm{\alpha}\right)-{f}_{\mathit{YZ}}^{\left(\mathrm{MIN}\right)}}{{f}_{\mathit{YZ}}^{\left(\mathrm{MAX}\right)}-{f}_{\mathit{YZ}}^{\left(\mathrm{MIN}\right)}},$$
(2)
$${f}_{\mathrm{\alpha}}\left({\mathrm{\theta}}_{\mathrm{\alpha}}\right)={f}_{\mathit{XY}}\left(\mathrm{\theta}_{\mathrm{\alpha}}{}^{\mathit{XY}}\right)\mathrm{\xi}+{f}_{\mathit{XZ}}\left(1-\mathrm{\xi}\right),$$
(3)
$$I\left({\mathrm{\theta}}_{\mathit{XY}}^{\prime}\right)={k}_{\mathit{XY}}\left[{a}_{\mathit{XY}}+\frac{{b}_{\mathit{XY}}}{1+exp\left(-\frac{{\mathrm{\theta}}_{\mathit{XY}}^{\prime}-{c}_{\mathit{XY}}}{{d}_{\mathit{XY}}}\right)}\right],$$
(4)
$$I\left({\mathrm{\theta}}_{\mathit{XZ}}^{\prime}\right)={k}_{\mathit{XZ}}\left\{{a}_{\mathit{XZ}}+\frac{{b}_{\mathit{XZ}}}{1+{\left({\mathrm{\theta}}_{\mathit{XZ}}^{\prime}/{c}_{\mathit{XZ}}\right)}^{{d}_{\mathit{xz}}}}+{e}_{\mathit{XZ}}+{f}_{\mathit{XZ}}exp\left[-\frac{1}{2}{\left(\frac{{\mathrm{\theta}}_{\mathit{XZ}}^{\prime}-{g}_{\mathit{XZ}}}{{h}_{\mathit{XZ}}}\right)}^{2}\right]\right\},$$
(5)
$$I\left({\mathrm{\theta}}_{\mathit{YZ}}\right)={k}_{\mathit{YZ}}\left(\frac{{a}_{\mathit{YZ}}+{b}_{\mathit{YZ}}{\mathrm{\theta}}_{\mathit{YZ}}+{c}_{\mathit{YZ}}\mathrm{\theta}_{\mathit{YZ}}{}^{2}}{1+{b}_{\mathit{YZ}}{\mathrm{\theta}}_{\mathit{YZ}}+{d}_{\mathit{YZ}}\mathrm{\theta}_{\mathit{YZ}}{}^{2}}\right).$$